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Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel

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Manat
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Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   Updated on: 17 Jan 2019, 21:38
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Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?

A) 1/4
B) 1/6
C) 1/8
D) 13/6
E) 6/13
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E

Originally posted by Manat on 17 Jan 2019, 19:09.
Last edited by Bunuel on 17 Jan 2019, 21:38, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   17 Jan 2019, 21:45
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Manat wrote:
Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?

A) 1/4
B) 1/6
C) 1/8
D) 13/6
E) 6/13


The combined rate of the three machines is 1/4 + 1/6 + 1/8 = 13/24 work/hour. So, working together they can do the job in 24/13 hours. In this time the fastest machine, the one that can do the job in 4 hours, would have done 1/4*24/13 = 6/13 part of the job (job done = rate*time).

Answer: E.

P.S. Please name topics properly. Check rule 3 here: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   17 Jan 2019, 19:16
Manat wrote:
Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?

A) 1/4
B) 1/6
C) 1/8
D) 13/6
E) 6/13


Are you getting B ??

= 4 / 24
= 1 / 6
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   17 Jan 2019, 20:07
Yes i got B. if the question had mentioned what part of the work is done in 1 hour, then i would have chosen 6/13 the OA. Confused

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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   17 Jan 2019, 20:19
Manat wrote:
Yes i got B. if the question had mentioned what part of the work is done in 1 hour, then i would have chosen 6/13 the OA. Confused

Posted from my mobile device


IMO, the question has not asked that.

Lets see if someone else adds something to this. :)
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   17 Jan 2019, 20:46
chetan2u Bunuel :-Could you please confirm if OA is correct?
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   17 Jan 2019, 21:51
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Manat wrote:
chetan2u Bunuel :-Could you please confirm if OA is correct?

The OA is correct..

Each working together, the work can be done in
(1/4)+(1/6)+(1/8)=13/24th work in one hour, so complete work in 24/13 hour..
Now the fastest machine can do the work in 4 hours so in 24/13 hours he can do (1 hour work)*(number of hours)=(1/4)*(24/13)=6/13..

Also how can fastest machine do just 1/6 of work, which means someone will do more than 1/6 of work. But fastest should do the maximum portion of work...
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   18 Jan 2019, 04:43
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Manat wrote:
Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?

A) 1/4
B) 1/6
C) 1/8
D) 13/6
E) 6/13



total rate of three machines = 1
so part of rate done by each machine = 13/24
and total time : 24/13
work done by fastest machine would be the one which has lowest hrs i.e 4 and rate : 1/4
so work of machine = rate * time = 24 /13*1/ 4= 6/13 IMO E
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Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   18 Jan 2019, 05:13
Really you can answer this question using the provided options and logic without ever doing any math.

There are 3 machines completing 1 task, if all machines worked at the same pace they would each complete 1/3 of the task. We know that 1 of the machines is the fastest and therefore will complete more than 1/3rd of the task because it is more productive than the others. This immediately eliminates A, B, and C as all are less than 1/3. D is eliminated because a machine cannot complete more than 100% of the task. Thus E is the only possible answer.

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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   18 Jan 2019, 07:35
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Manat wrote:
Yes i got B. if the question had mentioned what part of the work is done in 1 hour, then i would have chosen 6/13 the OA. Confused

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Afterall the OA was correct.

I again took an attempt at it, I solved it at paper this time( last time i didn't)

Work = rate * time

Total Time = 1/4 + 1/6 + 1/ 8 = 13/24

Took W as 1

Now if we take work as W, then rate = 24 / 13

Now what part of the finished work does the fastest machine do will be
rate * time
=> 24/13 * 1/4
=> 6/13
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   19 Jan 2019, 11:30
given that each machine completes the work in that many hours. not the rate of work done by each machine.
rate of work done by each machine
A- 1/4
B-1/6
C-1/8

TOTAL work done by three machines in one hour is equal to combined rates of work
1/4+1/6+1/8=13/24

fastest machine is the one which completes the work in shortest time i.e. 1/4

asked about the part by whole
(1/4)/(13/24)=6/13
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   20 Jan 2019, 09:04
Manat wrote:
Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?

A) 1/4
B) 1/6
C) 1/8
D) 13/6
E) 6/13


Let the total work be 24 (LCM of 4,6 & 8)

Efficiency of the 3 machines are 6 , 4 & 3

Thus, part of the finished work done by the fastest worker is \(\frac{6}{( 6+ 4 + 3)} = \frac{6}{13}\)

Fastest Worker = Worker having the highest efficiency

Thus, Answer must be (E)
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   22 Jan 2019, 10:06
time is taken by machines 4, 6 & 8 hours to complete a task individuality
it means their efficiencies are 6 / 4 / 3 (Because LCM is 24 for 4,6 and 8 and 24 is further divided by 4 /6/ 8 )

Hence, 6/6+4+3 gives 6/13 (a portion of the fastest machine)
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   19 Jan 2020, 07:54
Manat wrote:
Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?

A) 1/4
B) 1/6
C) 1/8
D) 13/6
E) 6/13


r=w/t
work together, then must add rates:
1/4+1/6+1/8…lcm(4,6,8)=(8*3)=24
24/4=6…24/6=4…24/8=3…numerator=6+4+3=13
rates together: 13/24;

time=work/rate:
time = 1 job / 13/24 = 24/13 hours
fastest machine's rate = 1/4
fastest mac's part of job = 1/4*24/13 = 6/13

Ans (E)
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   19 Jan 2020, 10:04
Manat wrote:
Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?

A) 1/4
B) 1/6
C) 1/8
D) 13/6
E) 6/13


Work done by fastest machine A in one hour = 1/4 = 6/24
Work done by all machines working together in one hour = 1/4 + 1/6 + 1/8 = 13/24
Part of the work done by A = 6/13

IMO E

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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink] New post   29 Nov 2022, 01:02
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel [#permalink]
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